docs: def execute(self, style, xpoints, ypoints, mask=None,
                  backend='vectorized', specified_drift_arrays=None):
          """Calculates a kriged grid and the associated variance.
          Includes drift terms.
  
          This is now the method that performs the main kriging calculation.
          Note that currently measurements (i.e., z values) are considered
          'exact'. This means that, when a specified coordinate for interpolation
          is exactly the same as one of the data points, the variogram evaluated
          at the point is forced to be zero. Also, the diagonal of the kriging
          matrix is also always forced to be zero. In forcing the variogram
          evaluated at data points to be zero, we are effectively saying that
          there is no variance at that point (no uncertainty,
          so the value is 'exact').
  
          In the future, the code may include an extra 'exact_values' boolean
          flag that can be adjusted to specify whether to treat the measurements
          as 'exact'. Setting the flag to false would indicate that the variogram
          should not be forced to be zero at zero distance (i.e., when evaluated
          at data points). Instead, the uncertainty in the point will be equal to
          the nugget. This would mean that the diagonal of the kriging matrix
          would be set to the nugget instead of to zero.
  
          Parameters
          ----------
          style : str
              Specifies how to treat input kriging points. Specifying 'grid'
              treats xpoints and ypoints as two arrays of x and y coordinates
              that define a rectangular grid. Specifying 'points' treats xpoints
              and ypoints as two arrays that provide coordinate pairs at which
              to solve the kriging system. Specifying 'masked' treats xpoints and
              ypoints as two arrays of x and y coordinates that define a
              rectangular grid and uses mask to only evaluate specific points
              in the grid.
          xpoints : array_like, shape (N,) or (N, 1)
              If style is specific as 'grid' or 'masked', x-coordinates of
              MxN grid. If style is specified as 'points', x-coordinates of
              specific points at which to solve kriging system.
          ypoints : array-like, shape (M,) or (M, 1)
              If style is specified as 'grid' or 'masked', y-coordinates of
              MxN grid. If style is specified as 'points', y-coordinates of
              specific points at which to solve kriging system.
              Note that in this case, xpoints and ypoints must have the same
              dimensions (i.e., M = N).
          mask : boolean array, shape (M, N), optional
              Specifies the points in the rectangular grid defined by xpoints and
              ypoints that are to be excluded in the kriging calculations.
              Must be provided if style is specified as 'masked'. False indicates
              that the point should not be masked, so the kriging system will be
              solved at the point. True indicates that the point should be masked,
              so the kriging system should will not be solved at the point.
          backend : str, optional
              Specifies which approach to use in kriging. Specifying 'vectorized'
              will solve the entire kriging problem at once in a vectorized
              operation. This approach is faster but also can consume a
              significant amount of memory for large grids and/or large datasets.
              Specifying 'loop' will loop through each point at which the kriging
              system is to be solved. This approach is slower but also less
              memory-intensive. Default is 'vectorized'.
              Note that Cython backend is not supported for UK.
          specified_drift_arrays : list of array-like objects, optional
              Specifies the drift values at the points at which the kriging
              system is to be evaluated. Required if 'specified' drift provided
              in the list of drift terms when instantiating the UniversalKriging
              class. Must be a list of arrays in the same order as the list
              provided when instantiating the kriging object. Array(s) must be
              the same dimension as the specified grid or have the same number of
              points as the specified points; i.e., the arrays either must be
              shape (M, N), where M is the number of y grid-points and N is the
              number of x grid-points, or shape (M, ) or (N, 1), where M is the
              number of  points at which to evaluate the kriging system.
  
          Returns
          -------
          zvalues : ndarray, shape (M, N) or (N, 1)
              Z-values of specified grid or at the specified set of points.
              If style was specified as 'masked', zvalues will be a numpy
              masked array.
          sigmasq : ndarray, shape (M, N) or (N, 1)
              Variance at specified grid points or at the specified set of points.
              If style was specified as 'masked', sigmasq will be a numpy
              masked array.
          """
  
          if self.verbose:
              print("Executing Universal Kriging...\n")
  
          if style != 'grid' and style != 'masked' and style != 'points':
              raise ValueError("style argument must be 'grid', 'points', "
                               "or 'masked'")
  
          n = self.X_ADJUSTED.shape[0]
          n_withdrifts = n
          xpts = np.atleast_1d(np.squeeze(np.array(xpoints, copy=True)))
          ypts = np.atleast_1d(np.squeeze(np.array(ypoints, copy=True)))
          nx = xpts.size
          ny = ypts.size
          if self.regional_linear_drift:
              n_withdrifts += 2
          if self.point_log_drift:
              n_withdrifts += self.point_log_array.shape[0]
          if self.external_Z_drift:
              n_withdrifts += 1
          if self.specified_drift:
              n_withdrifts += len(self.specified_drift_data_arrays)
          if self.functional_drift:
              n_withdrifts += len(self.functional_drift_terms)
          a = self._get_kriging_matrix(n, n_withdrifts)
  
          if style in ['grid', 'masked']:
              if style == 'masked':
                  if mask is None:
                      raise IOError("Must specify boolean masking array when "
                                    "style is 'masked'.")
                  if mask.shape[0] != ny or mask.shape[1] != nx:
                      if mask.shape[0] == nx and mask.shape[1] == ny:
                          mask = mask.T
                      else:
                          raise ValueError("Mask dimensions do not match "
                                           "specified grid dimensions.")
                  mask = mask.flatten()
              npt = ny*nx
              grid_x, grid_y = np.meshgrid(xpts, ypts)
              xpts = grid_x.flatten()
              ypts = grid_y.flatten()
  
          elif style == 'points':
              if xpts.size != ypts.size:
                  raise ValueError("xpoints and ypoints must have same "
                                   "dimensions when treated as listing "
                                   "discrete points.")
              npt = nx
          else:
              raise ValueError("style argument must be 'grid', 'points', "
                               "or 'masked'")
  
          if specified_drift_arrays is None:
              specified_drift_arrays = []
          spec_drift_grids = []
          if self.specified_drift:
              if len(specified_drift_arrays) == 0:
                  raise ValueError("Must provide drift values for kriging points "
                                   "when using 'specified' drift capability.")
              if type(specified_drift_arrays) is not list:
                  raise TypeError("Arrays for specified drift terms must be "
                                  "encapsulated in a list.")
              for spec in specified_drift_arrays:
                  if style in ['grid', 'masked']:
                      if spec.ndim < 2:
                          raise ValueError("Dimensions of drift values array do "
                                           "not match specified grid dimensions.")
                      elif spec.shape[0] != ny or spec.shape[1] != nx:
                          if spec.shape[0] == nx and spec.shape[1] == ny:
                              spec_drift_grids.append(np.squeeze(spec.T))
                          else:
                              raise ValueError("Dimensions of drift values array "
                                               "do not match specified grid "
                                               "dimensions.")
                      else:
                          spec_drift_grids.append(np.squeeze(spec))
                  elif style == 'points':
                      if spec.ndim != 1:
                          raise ValueError("Dimensions of drift values array do "
                                           "not match specified grid dimensions.")
                      elif spec.shape[0] != xpts.size:
                          raise ValueError("Number of supplied drift values in "
                                           "array do not match specified number "
                                           "of kriging points.")
                      else:
                          spec_drift_grids.append(np.squeeze(spec))
              if len(spec_drift_grids) != len(self.specified_drift_data_arrays):
                  raise ValueError("Inconsistent number of specified drift "
                                   "terms supplied.")
          else:
              if len(specified_drift_arrays) != 0:
                  warnings.warn("Provided specified drift values, but "
                                "'specified' drift was not initialized during "
                                "instantiation of UniversalKriging class.",
                                RuntimeWarning)
  
          xy_points_original = \
              np.concatenate((xpts[:, np.newaxis], ypts[:, np.newaxis]), axis=1)
          xpts, ypts = _adjust_for_anisotropy(np.vstack((xpts, ypts)).T,
                                              [self.XCENTER, self.YCENTER],
                                              [self.anisotropy_scaling],
                                              [self.anisotropy_angle]).T
          xy_points = \
              np.concatenate((xpts[:, np.newaxis], ypts[:, np.newaxis]), axis=1)
          xy_data = np.concatenate((self.X_ADJUSTED[:, np.newaxis],
                                    self.Y_ADJUSTED[:, np.newaxis]), axis=1)
  
          if style != 'masked':
              mask = np.zeros(npt, dtype='bool')
  
          bd = cdist(xy_points,  xy_data, 'euclidean')
          if backend == 'vectorized':
              zvalues, sigmasq = self._exec_vector(a, bd, xy_points,
                                                   xy_points_original,
                                                   mask, n_withdrifts,
                                                   spec_drift_grids)
          elif backend == 'loop':
              zvalues, sigmasq = self._exec_loop(a, bd, xy_points,
                                                 xy_points_original,
                                                 mask, n_withdrifts,
                                                 spec_drift_grids)
          else:
              raise ValueError('Specified backend {} is not supported '
                               'for 2D universal kriging.'.format(backend))
  
          if style == 'masked':
              zvalues = np.ma.array(zvalues, mask=mask)
              sigmasq = np.ma.array(sigmasq, mask=mask)
  
          if style in ['masked', 'grid']:
              zvalues = zvalues.reshape((ny, nx))
              sigmasq = sigmasq.reshape((ny, nx))
  
          return zvalues, sigmasq